Steven, list,>[Steven] My point to Ben is only that you cannot put a smattering of "some" around such definitions. [End quote]
Steven, if you want more formal definitions of the distinctions, look to the table of summary of properties that I provided in the same initial post in this thread.
I defined the deductive-ampliative distinction as fully, even more fully, than Peirce did. This is, or has become, pretty elementary stuff. There is no need to provide specific formalizations of modes of inference in order to do that much. All you need are the ideas of premisses (when conjoined) and conclusion, and the idea of entailment a.k.a. deductive implication, the deductive validity of the conditional, or truth-preservativeness. There is no need for me to define those things all over again; they have been defined many times, in various perspectives, especially proof-theoretic and model-theoretic, with the same inferences being sorted into the same classes deductive and non-deductive (a.k.a. ampliative), as a result. It would not be to the purpose for me to state forms of deduction when there is no general disagreement about what is deductive in classical, two-valued logic. There is also another distinction, quite analogous, between an inference whose conclusion entails its premisses and an inference whose conclusion does not entail its premisses, and the preceding part of this sentence is all the formalization needed for the purpose. My point was to have single generic _/words/_ to express that distinction, not to introduce some new or difficult distinction that nobody had ever thought of. With those two distinctions into _/named/_ classes, one has a complete set of names, labels, for simple classes of inferences according to entailment relations and truth/falsity-preservation between (A) the premisses when conjoined and (B) the conclusion. I don't scorn further formalization. The whole point is for dealing with further formalizations.
That is because, then, one can look at _/various/_ formalizations of various modes of inference such as deduction, induction, and abduction, and have a fuller set of words to discuss how they end up classified in terms of such entailment relations and truth/falsity-preservation. The whole point was to provide a bit of _/terminology/_ for future discussion OF formalizations. When I hit upon the word 'attenuative', I thought, well that's much better for the purpose than the words 'reductive' and 'precisive' would be. The more I thought about it, the worse for the purpose 'precisive' seemed. And 'reductive' is hairy with topical connotations from other contexts.
Now, I had tended to think of induction as ampliative, but still as not 'attenuative' but 'repletive' - as being such that its conclusion entails its premisses. But when I considered Peirce's over-the-years formalizations of induction, and many common examples usually regarded as inductive, I realized that, at least as framed, most of them in fact made induction attenuative as well as ampliative. So, if I want to save the idea that, 'in the fields of light', induction, as commonly understood, is repletive, not attenuative, _/that's when I would need to offer a formalization of it/_ - one wherein it is repletive yet captures what is really needed for the idea of induction as formalized by Peirce and others. If I do that, the words 'attenuative' and 'repletive' will come in handy, so that I don't need to keep using _/long phrases/_ like 'whose conclusion doesn't entail its premisses' and 'whose conclusion does entail its premisses'.
Best, Ben On 4/8/2015 12:03 PM, Steven Ericsson-Zenith wrote:
I am only thinking of the formalization of deduction. What problem do you see, exactly?My point to Ben is only that you cannot put a smattering of "some" around such definitions.Regards, StevenOn Wed, Apr 8, 2015 at 8:19 AM, Jerry LR Chandler <[email protected] <mailto:[email protected]>> wrote:Steven: I was slightly stunned by your response. When you write:I am thinking only of Babara as the starting point.I wondered if this broad assertion refers to your views on biophysics as well (either inferring FOL or not)? Cheers Jerry On Apr 8, 2015, at 10:03 AM, Steven Ericsson-Zenith wrote:I am thinking only of Babara as the starting point. StevenOn Tue, Apr 7, 2015 at 10:12 PM, Jerry LR Chandler <[email protected] <mailto:[email protected]>> wrote: Ben, Steven, List: Ben: Thanks for the update on your views. I will think about your categorization for a bit and respond if anything trivial or better comes to mind. Thanks for the reference to Kant. I have been digging a bit further myself, but got side-tracked by the more general problem of the semantics of logic itself. Although my knowledge of German is scant, my recall suggests that CSP did not choose the best term for translation. But, see 4.43. where CSP states rather clearly the basis for his disagreement with Kant's terminology, that is Kant's notion of 'synthetic' reasoning. What is important in this passage is that CSP asserts the classification of propositions is by "per se" or "per accidens", drawing upon the Isagoge of Porphyry! So that gives us one historical path from Aristotle's view to the present day. The meaning of "ampliative" (as I was using it) was in the sense of "per accidens'. My thinking about the term "ampliative" was by assuming that the term was a sibling to the term 'amplification' and its well defined technical meaning in both mathematics and wave mechanics. Consequently, I associated 'ampliative' with ratiocination and the notion of proof theory of going from the known to the unknown. It is in this sense that I concluded that > the ampliative conclusion deductively implies the premisses. because this is true for the proof theory of chemical relations. In this form of proof theory for chemical structures, the validity of the assertion lies in the conservation laws of physics and concurrence of measurements of mass and charge in atoms and the molecules composed from them. The "abductive logic" is in the postulation of a particular structure from a set of atoms. This ampliative wrt to size of the molecule. Steven: Your assertion that: "Deduction has been formalized since Aristotle." is a bit strong, isn't it? The hybrid logics of T. Brauner offer relations between deductions and proof theories as being term dependent in the sense of Kripke semantics. BTW, at the moment at least, I really like the approaches of Brauner, which bases the method of proof on the meaning of the terms. And, rather remote from Aristotle's sorites. The gaps between Danko's cybernetics and "Natural Propositions" and Brauner's hybrid logic are obvious. But, as of now, I have not found any obvious conceptual gaps between Brauner's Hybrids and chemical proof structures. VERY exciting to me! Cheers Jerry On Apr 7, 2015, at 12:51 PM, Benjamin Udell wrote:Jerry, list, I felt somewhat hampered in the discussion below by a lack of terminology. We have the words 'deductive' and 'ampliative' for inferences where the conclusions don't or do, respectively, add something beyond the premisses. But I can't find a generic word for an inference where the conclusion says _/at least as much as/_ the premisses say, nor a generic word for an inference where the conclusion _/omits/_ something that the premisses say. So I've come up with a couple of words - _/repletive/_ and _/attenuative/_ - that will come in handy if such discussion arises again, though such discussion doesn't arise often. ('Entail' = 'deductively imply'.) *Inferences: /Deductive/ = Everything* (explicit or entailed) *in the conclusion is* (explicit or entailed) *in the premisses.* */Ampliative/ = Something* (explicit or entailed) *in the conclusion is not* (explicit or entailed) *in the premisses.* */Repletive/ = Everything* (explicit or entailed) *in the premisses is* (explicit or entailed) *in the conclusion.* */Attenuative/ = Something* (explicit or entailed) *in the premisses is not* (explicit or entailed) *in the conclusion. * Inferences */Deductive:/* */Ampliative:/* */Repletive:/* *'Reversible' deduction. * *Some induction. * */Attenuative:/* *'Forward-only' deduction. * *Abduction, much induction*. * *E.g., "3/5 of the sample is blue, so (likely) 3/5 of the total is blue" is usually considered inductive. Still, it's not only ampliative, it's also attenuative. Summary of properties from perspectives of proof theory and model theory (not that I know much about them) . Inferences ⇓ */Proof-theoretic perspective:/* */Model-theoretic perspective: /* */Deductive:/* Premisses *entail* conclusions. Automatically *preserves truth*. /*Ampliative* (i.e., non-deductive)*:*/ Premisses *do not entail* conclusions. *Does not* automatically *preserve truth*. */Repletive:/* Premisses *are entailed by* conclusions. Automatically *preserves falsity*. /*Attenuative* (i.e., non-repletive)*:*/ Premisses *are not entailed by* conclusions. *Does not* automatically *preserve falsity*. Best, Ben *Subject:* Re: [PEIRCE-L] Bayes and abduction - from the perspective of organic mathematics / the unity of the sciences *Date:* Mon, 06 Apr 2015 14:00:32 -0400 *From:* Benjamin Udell *To:* [email protected] <mailto:[email protected]>Jerry, all, Jerry, I can't address the things you say about chemistry, I don't have the background. But I can say some things about Peirce's examples of abductive and inductive inferences. Jerry, you wrote, CSP's usage of the term ampliative infers that: > the ampliative conclusion deductively implies the premisses. In most of Peirce's examples (e.g., 1867, 1878, 1883) that I've seen, neither the inductive conclusion usually nor the abductive conclusion ever deductively implies its premisses. So it seems unlikely that he thought the term "ampliative", as applied to inference, meant that the conclusion deductively implies the premisses. Anyway he says that non-deductive inferences are ampliative and that this means that "they conclude something not implied in the premisses" in "The Doctrine of Necessity Examined" (1892, see CP 6.40 http://www.iupui.edu/~arisbe/menu/library/bycsp/necessity/necessity.htm <http://www.iupui.edu/%7Earisbe/menu/library/bycsp/necessity/necessity.htm> ). Obviously, just in order to be non-deductive, a non-deductive inference does not have to have a conclusion that deductively implies its premisses. It just needs to have a conclusion that its premisses don't deductively imply. The inductive conclusion that all the beans from the bag are white does not deductively imply the premisses that these beans here are from the bag and that they are white. A rare exception is the crude induction of the kind (not Peirce's actual example), 'all swans in England are white, ergo all swans in the world are white' (except insofar as the conclusion fails to imply that there is an England; but one might get around that somehow). But if one says, 3/5 among all swans in England are white, ergo 3/5 among all swans in the world are white, then the conclusion does not deductively imply the premiss, yet the inference would usually be regarded as inductive (and hardly less crude than the first one). Can we get the deductiveness by adding qualifiers? If the conclusion is that it is _/likely/ _ that 3/5 among all swans in the world are white, that deductively implies at most that it is _/likely, but somewhat less likely,/ _ that 3/5 among all swans in England are white. And that was not the inductive premiss. A finding (predating the fame of black swans as in the above examples) might be stated carefully, "All swans in Europe are white, ergo all swans in Europe and very likely all swans elsewhere, are white." There the conclusion deductively implies the premiss, by repeating it somewhat crudely. Still (and I don't know what Peirce would think of this), maybe that's more in the spirit of an inductive conclusion, painting a fuller picture of a total population, showing observations and predictively extended trend line together; the extended trend line all by itself might be taken as a weakly abductive (non-explanatory and involving no new or outside idea) statistical hypothesis of some sort, the interest in it remaining grounded in interest in the particular population under observation; so maybe the "really" inductive conclusion is observations plus extended trend line. On the other hand, the inquirial interest of an abductively conceived theory like general relativity goes beyond the inquirial interest of the Sun and any actual stars around which gravitation's bending of light is observed; the theory's conclusions are stated in general forms without mention of the Sun etc. But I admit that I'm trying to get at things here that I'm not quite clear on. As to abducing particulars, one sees the lawn wet one morning, considers that, as a matter of course, if it rains at night, the lawn is wet the next morning, and concludes that very plausibly it rained last night - which conclusion does not deductively imply its premisses. To check the conclusion, one might check neighboring lawns. The interest has become whether it rained last night, not the total set of nights and mornings at the lawn, nor just the condition of one's own lawn. A rainfall last night might explain many things. So it doesn't make sense to recast the conclusion in some premisses-implying form like "it rained last night and my lawn is wet, and that happens as a matter of course, with night rain never failing to leave my lawn wet." Best, Ben On 4/6/2015 12:39 AM, Jerry LR Chandler wrote:List, Ben, Clark, Danko: On Apr 3, 2015, at 1:04 PM, Benjamin Udell wrote:Peirce also characterizes non-deductive inference as _/ampliative/ _, that is, having conclusions not deductively implied by the premisses, and I still like the idea, that I had before reading Peirce, of distinguishing induction from more 'leapy' or conjectural inference, by whether the ampliative conclusion deductively implies the premisses or not (I've tended in the past to speak of 'surmise' when I've had in mind conjectural inference so defined, because I've doubted that people would agree to define abduction as inference that lacks deductive implication whether by premisses of conclusions or vice versa). Now, it's easy enough to come up with an ampliative conclusion; such a conclusion doesn't need abductive plausibility or Peirce's inductive verisimilitude (the likeness of the conclusion to the premissual samples) in order to be ampliative; but, without them, it just isn't intrinsically fruitful or promising in inquiry. Likewise a deductive conclusion can simply repeat a premiss word for word and still be deductive, but such a deduction, lacking any new or nontrivial aspect, just isn't intrinsically fruitful or promising in inquiry.First, thanks to you, Ben, I have studied the potential meaning of the logical term, ampliative, for nigh unto a decade now, perhaps longer. At this point in time, one firm conclusion about CSP's usage of this term is clear, at least in my mind, with respect to the life sciences. Within the framework of the explicit sortal logic of chemistry, molecular biology, and the pan-chemical sciences, CSP's usage of the term ampliative infers that:the ampliative conclusion deductively implies the premisses.Within the Peircian mathematical / philosophical context, this conclusion is a central component of the trichotomy components, sin-sign, index, icon, Rheme and Dicisign *with respect to* the legisign as well as organic mathematics As I have asserted before, the trichotomy is an example of chemical reasoning that is extensible. Within the sortal logic of organic mathematics, the legisign (natural law in the sense of Kant?) includes the concepts of atomic masses and valence. In this case, I simply assert that sin-sign of a molecule, as representations of the forms of atomic weights, is a basis of CSP's central term "index." This basic logical chemical operation of addition of atomic weights is physically measured as a quali-sign of a molecular sin-sign. /Both the qualisign and index are quantitative predicates of logical propositions of a molecular sin-sign. / In the modern chemical icon (structure), these physically measured quantities, take on the form of a diagram, a graph, and, yet, more specifically, a labelled bipartite graph, a connected lattice of electrical relations that serves as the initial conditions for quantum mechanical calculations. In this context, these terms all describe mathematical terms relatable to the the index. /Thus, I conclude that the Peircian term, ampliative, adroitly coheres with the logical unity of the natural sciences because of the physical logical connection between the sin-sign and it's index./ [.....] Cheers Jerry
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